The \({\cal N}=1\)  super-Cotton tensor [1]} is given by the expression
\({\cal W}_{\alpha \beta \gamma } = \Big (\frac{{\rm i}}{2} {\cal D}^2 +4{\cal S}\Big ) {\cal C}_{\alpha \beta \gamma }+ {\rm i}{\cal D}_{(\alpha \beta } {\cal D}_{\gamma )} {\cal S}~.\) 
